Looking for Compatible Routes in the Railway Interlocking System of an Overtaking Station Using a Computer Algebra System

The author has a long experience in railway engineering software development, mainly using computer algebra systems. Now a software package that allows the user to obtain compatible routes in an overtaking station of any number of tracks and any topology, based in dealing with cycles, has been developed. It has been implemented in the computer algebra system Maple and takes advantage of its GraphTheory package. There are two main uses of such a package. One is complementing topology independent railway interlocking systems, providing alternative routes. The other is to easily explore alternative track layouts. The package can only deal with overtaking stations (the most common ones in double track lines). Note that the latter use is important: for instance, the Spanish infrastructure administrator is nowadays remodeling the track layouts of the main railway stations of Madrid, Seville and Barcelona.